If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expectation of this
Game?
A) -$2.78
B) $3.06
C) -$3.06
D) $2.78

Question

Quizplus · Accepted Answer

The expectation can be calculated by finding the probability of each outcome, multiplying each by its corresponding payoff, and summing these products. The probability of rolling a sum of 10 with two dice is 3/36 (or 1/12), since the combinations (4,6), (5,5), and (6,4) can result in a sum of 10. The probability of rolling a sum of 3 is 2/36 (or 1/18), with the combinations (1,2) and (2,1). The expected winnings are thus (3/36)*$10 + (2/36)*$20. However, since the cost to play is $5, this cost must be subtracted from the expected winnings. The calculation is: [(3/36)*$10 + (2/36)*$20] - $5 = -$3.06.

If a Gambler Rolls Two Dice and Gets a Sum